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Detective Senior Sergeant Craig Johnson says emergency services were called to the Countdown carpark in Moorhouse Ave, in the suburb of Sydenham, about 2am after a man was found with serious injuries.
"He was transported to hospital where he remains in a critical condition."
Det Johnson said inquiries have begun to establish what happened and who was responsible.
A scene examination is under way in the carpark area.
Anyone with information is asked to contact police on 105 and quote event number P048837013.
Information can also be provided anonymously via Crime Stoppers on 0800 555 111.